Research Papers

Size-Dependent Elasticity of Nanoporous Materials Predicted by Surface Energy Density-Based Theory

[+] Author and Article Information
Yin Yao

Institute of Advanced Structure Technology,
Beijing Institute of Technology,
Beijing 100081, China;
Beijing Key Laboratory of Lightweight
Multi-functional Composite Materials
and Structures,
Beijing Institute of Technology,
Beijing 100081, China

Yazheng Yang

Institute of Advanced Structure Technology,
Beijing Institute of Technology,
Beijing 100081, China;
Beijing Key Laboratory of Lightweight
Multi-functional Composite Materials
and Structures,
Beijing Institute of Technology,
Beijing 100081, China;
Collaborative Innovation Center
of Electric Vehicles in Beijing,
Beijing Institute of Technology,
Beijing 100081, China

Shaohua Chen

Institute of Advanced Structure Technology,
Beijing Institute of Technology,
Beijing 100081, China;
Beijing Key Laboratory of Lightweight
Multi-functional Composite Materials
and Structures,
Beijing Institute of Technology,
Beijing 100081, China;
Collaborative Innovation Center
of Electric Vehicles in Beijing,
Beijing Institute of Technology,
Beijing 100081, China
e-mail: chenshaohua72@hotmail.com

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received February 25, 2017; final manuscript received March 16, 2017; published online April 18, 2017. Editor: Yonggang Huang.

J. Appl. Mech 84(6), 061004 (Apr 18, 2017) (8 pages) Paper No: JAM-17-1109; doi: 10.1115/1.4036345 History: Received February 25, 2017; Revised March 16, 2017

The size effect of nanoporous materials is generally believed to be caused by the large ratio of surface area to volume, so that it is also called surface effect. Based on a recently developed elastic theory, in which the surface effect of nanomaterials is characterized by the surface energy density, combined with two micromechanical models of composite materials, the surface effect of nanoporous materials is investigated. Closed-form solutions of both the effective bulk modulus and the effective shear one of nanoporous materials are achieved, which are related to the surface energy density of corresponding bulk materials and the surface relaxation parameter of nanomaterials, rather than the surface elastic constants in previous theories. An important finding is that the enhancement of mechanical properties of nanoporous materials mainly results from the compressive strain induced by nanovoid's surface relaxation. With a fixed volume fraction of nanovoids, the smaller the void size, the harder the nanoporous material will be. The results in this paper should give some insights for the design of nanodevices with advanced porous materials or structures.

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Grahic Jump Location
Fig. 2

Schematics of a representative volume element for a porous material with spherical nanovoids: (a) a RVE, in which the nanovoid has a radius r1 and a volume V1, the matrix has a radius r2 and a volume V2 with a boundary S and (b) a Cartesian coordinate system {x1, x2, x3} and a spherical one {r, θ, φ} attached to a nanovoid

Grahic Jump Location
Fig. 1

Schematic of a surface unit cell in the initial (reference), relaxed, and current configurations, where a local coordinate system (1, 2) coincides with the bond directions

Grahic Jump Location
Fig. 3

Normalized effective bulk modulus and shear one of Al-based nanoporous materials as a function of void radius. The numerical results (solid dots and hollowed circles) obtained by finite element method based on the surface elasticity theory are also presented for comparison.

Grahic Jump Location
Fig. 4

Comparison of the dilute solution obtained in the RVE model with an infinite matrix assumption and the nondilute one in the RVE model with a finite-sized matrix for Al-based nanoporous materials: (a) for the normalized effective bulk modulus and (b) for the normalized effective shear modulus



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